Collision of a particle with a thin rod

[Satvik Pandey]

Imagine that you kick a ball towards a wall perpendicularly. The ball rolls before hitting the wall. There is friction between the wall and the ball. What happens during the impact? What forces are exerted on the ball? How will it move after the impact?

As ball collides the velocity of it's CoM changes it's direction but the angular velocity doesn't. So the ball tends to move left after the collision however $\omega$ remains in the same direction. So the lower end of the ball slips on the ground so $\mu_{k}mg$ acts at the bottom of the ball to the right. As the vertical wall is rough so vertical component of impulse acting on it will be $\mu_{k}J$ if the ball slides on the wall during collision. I think it will bounce after collision.

This article looks interesting, I have not read it yet.
http://www.physics.usyd.edu.au/~cross/Gripslip.pdf

Thanks for the video and article. The video is amazing. I will surely read that article.:)

 

[ehild]

View attachment 78041
As ball collides the velocity of it's CoM changes it's direction but the angular velocity doesn't.

What impulsive torque acts on the ball during impact? Does it not change the angular velocity? How does it accelerate the CoM of the ball?

 

[Satvik Pandey]

What impulsive torque acts on the ball during impact? Does it not change the angular velocity? How does it accelerate the CoM of the ball?

The impulsive torque will be $\mu_{k}JR=J_{y}$ in anti clockwise direction. I have neglected the friction force at the bottom. I think it will be too small as compared to $\mu_{k}JR$. Can we do that? I have written a wrong statement. The angular velocity changes but I assume the direction of final angular velocity same as the initial.

So $\omega_{f}=\omega-\frac{\mu_{k}JR}{I}$

Let $V_{y}$ be the final velocity of the ball in Y-direction.

So $V_{y}=\frac{\mu_{k}J}{m}$

 

[ehild]

Will the ball bounce up a bit during the impact? I think it will. We need to do some experiments :)

 

[Satvik Pandey]

Will the ball bounce up a bit during the impact? I think it will. We need to do some experiments :)

But that doesn't effect the final velocity in Y direction (it will remain same as $\frac{\mu_{k}J}{m}$).right?

 

[ehild]

If the ball both rotates and slips during the impact, you do not know the direction of the relative velocity of the surface in contact with the wall. The force of friction opposes that relative velocity, but you do not know the direction.
And think of the tennis ball in the video. Nothing is sure what happens during an impact.

 

[Satvik Pandey]

I have a confusion regarding pure rolling motion.

In figure the ball's CoM has $v$ velocity and angular velocity is $\omega$. For pure rolling motion $v=r\omega$ must be true. Here there is +ve angular acceleration due to friction force but -ve acceleration of ball's CoM due to that force. In $dt$ time the angular acceleration will increase and velocity of ball's CoM will decrease. So the equation $v=r\omega$ will not hold for long. Where am I wrong in the logic?

 

[ehild]

I have a confusion regarding pure rolling motion.
View attachment 78179
In figure the ball's CoM has $v$ velocity and angular velocity is $\omega$. For pure rolling motion $v=r\omega$ must be true. Here there is +ve angular acceleration due to friction force but -ve acceleration of ball's CoM due to that force.

In case of pure rolling with constant velocity the friction is static, and the force of friction is zero.:)

 

[Satvik Pandey]

In case of pure rolling with constant velocity the friction is static, and the force of friction is zero.:)

Thank you! I got it. That was a silly question.